A Photon Computational Solution System for Differential Equations with Variable Coefficients

Abstract

The present invention discloses a variable coefficient differential equation photon computing solution system, which belongs to the field of photon computer technology. The system includes a microwave photon cascade modulator, input optical signal detection, a silicon-based microring resonator chip, a packaging scheme, and solved signal detection. The cascade modulator generates a time domain Gaussian pulse train, detects the time domain and frequency domain signals, inputs them into the packaged silicon-based microring resonator, performs numerical solution of the differential equation, solves the differential equation coefficients according to the detected frequency domain output signal, and the detected time domain signal is the numerical solution of the differential equation. The present invention can realize the rapid solution of the differential equation, and can realize the adjustment of the differential equation coefficients, and the numerical solution has high accuracy within the adjustable range of the coefficients.

Description

Technical Field

[0001] The invention relates to the technical field of photon computers, and in particular to a photon computing and solving system for differential equations with variable coefficients. Background Art

[0002] In recent years, with the continuous development of CMOS-based electronic chips, the size of electronic chips has approached the physical limit, and Moore's Law has gradually begun to no longer apply. With the advent of today's big data, artificial intelligence, and 5G era, the requirements for computing power are getting higher and higher. In 2019, Prune and others from Princeton University in the United States wrote an article pointing out that the demand for computing power in the era of artificial intelligence and big data doubles every three and a half months, far exceeding the computing power supply predicted by Moore's Law. The scientific community is looking for new ways to solve the computing power problem. Using photon computing to replace traditional electronic chip computing is currently proven to be one of the more effective methods to solve the problem of insufficient computing power in the dilemma of Moore's Law, and it is also one of the most promising ways to solve the power consumption problem.

[0003] Silicon-based photonic device integrated chips are developing rapidly due to their reliance on mature semiconductor process systems. Optical computing and information processing technologies based on silicon-based integrated photonic devices are the mainstream methods for solving future ultra-high-speed computing and information processing in the optical domain, and have very important applications and market value. Among the many silicon-based integrated photonic device structures, silicon-based microresonators not only have the advantages of compact size, flexible structure, and easy large-scale expansion, but also have the characteristics of wavelength selectivity, high quality factor, and resonance field intensity enhancement effect. Therefore, they are widely used in lasers, optical filters, electro-optic modulators, optical switches, optical delay lines, photodetectors, and sensors.

[0004] Differential equations were praised by the great scientist Newton as the language for describing the laws of nature. They have very wide applications in the modeling and analysis of natural sciences and engineering, and their application fields cover classical mechanics, circuit theory, cybernetics, molecular dynamics, weather forecasting and many other aspects. The calculation and solution of differential equations are important contents of modern signal processing. As the most basic differential equation, linear constant coefficient differential equations (ODE) are widely used in the mathematical modeling and theoretical analysis of linear time-invariant systems (LTI) and are the main research objects of classical signal and system theory. Solving differential equations with digital electronic computers requires high complexity, and the improvement of algorithms and computing speed has always been a problem to be solved. Summary of the invention

[0005] In view of this, the present invention provides a variable coefficient differential equation photon computing solution system. The system has good effect, is easy to implement, has ultra-high computing speed, and can adjust the value of the optical differential equation with the coefficient.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A variable coefficient differential equation photon computing solution system comprises a laser, a first modulator, a second modulator, a first amplifier, and a first filter connected in series in sequence; the first modulator is used to modulate an optical signal into a Gaussian function in the time domain; the second modulator is used to realize pulse cutting and is driven by a 10 GHz radio frequency signal emitted by a radio frequency source;

[0008] The other end of the first filter is connected to the input port of the 3D coupler; one output port of the 3D coupler is connected to the first oscilloscope, and the other output port is connected in sequence to the silicon-based micro-ring modulator chip, the second amplifier, the second filter and the second oscilloscope; the first oscilloscope is used to input the time domain excitation of the differential equation, the second oscilloscope is used to output the normalized numerical solution of the differential equation, and the silicon-based micro-ring modulator chip is used to numerically solve the differential equation.

[0009] Furthermore, the silicon-based microring resonator chip includes two parallel straight waveguides; a racetrack-type microring resonator coplanar therewith is provided between the two straight waveguides; electrodes for voltage heating are provided at the angles formed by the microring resonator and the straight waveguide; the incident end of the silicon-based microring resonator is a grating-based optical fiber array vertical coupling package, the electrical package is connected to a power supply, and the optical package output end is connected to an oscilloscope.

[0010] Furthermore, the 3D coupler can be replaced by a three-beam splitter.

[0011] Furthermore, the first output end and the second output end of the splitter / trimmer are respectively connected to the two corresponding output ends of the 3D coupler in the same manner; and the third output end of the splitter / trimmer is connected to the third spectrometer.

[0012] Furthermore, the optical packaging output end of the silicon-based microring resonator chip is connected to the input end of the beam splitter, and the two output ends of the beam splitter are respectively connected to the second oscilloscope and the second spectrometer.

[0013] Furthermore, polarization controllers are provided between the laser and the first modulator, between the first modulator and the second modulator, and between the 3D coupler and the silicon-based microring resonator chip.

[0014] The beneficial effects of the above technical solution of the present invention are:

[0015] The present invention constructs a generation module for a Gaussian pulse train input into a photon differential equation, detects the time domain and frequency domain spectra of an input optical signal, and constructs a silicon-based micro-ring resonator differential equation numerical solution system. Through the parameters of the micro-ring resonator and the on-chip electrode thermal adjustment method, and the fiber array vertically coupled grating packaging method, the electrical packaging adopts a wire bonding method, and the coefficients of the differential equation are obtained according to the output frequency domain spectrum. The output time domain spectrum is normalized to obtain the normalized numerical solution of the differential equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic diagram of an embodiment of the present invention.

[0017] Figure 2 It is a schematic diagram of an add-drop multiplexing silicon-based microring resonator.

[0018] Figure 3 Is for Figure 1 Schematic diagram of the silicon-based microring resonator chip.

[0019] Figure 4 4 is a graph showing the relationship between the coupling point temperature and the differential equation coefficients of the micro-ring modulator in an embodiment of the present invention.

[0020] Figure 5 This is the Gaussian pulse diagram of the cascade modulator obtained by simulation.

[0021] Figure 6 This is the simulation diagram of solving the differential equation of the Gaussian pulse obtained by simulation.

[0022] Figure 7 This is the basic structure diagram of a ring resonator.

[0023] Figure 8 It is a plug-and-drop multiplexing type micro-ring resonator. DETAILED DESCRIPTION

[0024] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0025] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0026] A photon computing solution system for differential equations with variable coefficients, referring to Figures 1 to 3The system includes: a laser, two modulators, a beam splitter, a filter, an amplifier, an oscilloscope, and a spectrometer. The silicon-based microring resonator chip includes: a straight waveguide, gratings at both ends, electrodes, optical and electrical packaging of the microring resonator and the chip. Finally, an oscilloscope and a spectrometer are installed to solve the coefficients of differential equations and detect numerical solutions.

[0027] The laser is cascaded with two modulators, and an amplifier, a filter, and a beam splitter are connected in sequence. The first output port of the beam splitter is connected to an oscilloscope, the second output port is connected to a spectrometer, and the third output port is connected to a polarization modulator and then to a packaged silicon-based microring resonator chip. The electrical package of the silicon-based microring resonator chip is connected to a multi-functional power supply, and the optical package output end is connected to a beam splitter, and then respectively connected to the oscilloscope and the spectrometer.

[0028] The silicon-based microring resonator chip is of bifurcated multiplexing type and racetrack type. The incident end is a vertically coupled package of a grating-based optical fiber array. The electrical package uses gold wire bonding to lead the electrodes to the PCB board for packaging.

[0029] The coefficients of the differential equation are obtained from the spectral lines measured by two spectrometers. According to the two frequency spectral lines corresponding to the same time, the frequency analysis of the transfer function of the entire microring resonator is performed. According to the obtained transfer function, the value of the coefficient of a constant coefficient differential equation solved by the microring resonator is obtained.

[0030] The reading of the oscilloscope before the input silicon-based microring resonator chip is the time domain excitation of the input differential equation, and the reading of the output oscilloscope is the normalized numerical solution of the output differential equation after normalization.

[0031] The silicon-based microring resonator chip requires an alignment waveguide for waveguide alignment during packaging, adjusting the six-position adjustment frame, and adjusting the polarization controller before the input end to adjust the polarization. After alignment, glue is dispensed and the optical fiber array is packaged.

[0032] The following are the specific implementation steps:

[0033] Step 1: Build a differential equation photon calculation solution system with variable coefficients as described above.

[0034] Step 2: Adjust the PPG and RF signals input to the modulator to modulate the output signal into a Gaussian pulse in the time domain.

[0035] Step 3: Align and package the silicon-based microring resonator chip, connect the input fiber array to the laser, connect the output to the power meter, adjust the polarization modulator, and align the fiber array with the six-position adjustment frame to maximize the power, and then package it.

[0036] Step 4: Process the frequency domain signal of the output signal of the resonator and the frequency domain signal of the input signal to obtain the coefficients of the differential equation to be solved.

[0037] Step 5: Normalize the obtained time domain signal, that is, solve the normalized differential equation.

[0038] Principle of this embodiment:

[0039] 1.1 Microring coupled mode theory

[0040] The basic structural unit of the silicon-based microring resonator is the optical waveguide that effectively confines the light field and transmits it in a direction. Its theoretical basis is the waveguide optics theory with Maxwell's equations as the core.

[0041] Reference Figure 7 When the silicon-based microresonator works under linear conditions, it can be equivalent to a linear analog filter, so it can be modeled using time domain coupling theory and frequency domain coupling theory.

[0042] Since the microring is a cyclic process of continuous dissipation of light, and a dissipative mode, the equation describing its dissipation is:

[0043]

[0044] This equation describes the process of continuous energy loss of the mode, where τ e represents the external loss, τ i is the loss inside the resonator, which mainly comes from the waveguide length inside the microring. Therefore, according to the microring resonator and the light field input condition, the above equation is rewritten to obtain:

[0045]

[0046] In the above formula, a is the energy amplitude within the ring, E i (t) is the electric field strength of the external excitation light field input, τ = 1 / (1 / τ i +1 / τ e ), μ is the conversion coefficient. The phase factor -j before μ can be arbitrarily selected according to the selected reference plane, which is determined by the consistency with the general spatial coupling mode. Due to the conservation of energy, the output electric field and the output electric field have the following conversion relationship:

[0047] E0(t)=E i (t)-jμa(t) (3)

[0048] When there is no light field input, that is, E i When (t) = 0, and assuming that there is an initial energy W0 in the microring resonator, the energy in the resonator changes with time as follows:

[0049]

[0050] Where E r (t) is the electric field strength in the resonator, T r is the time it takes for light to travel one circle in the ring. The energy in the ring is coupled to the straight waveguide and is continuously consumed. Therefore, the square of the electric field strength in the straight waveguide is the change of energy in the ring over time:

[0051]

[0052] Where κ is the coupling coefficient between the resonator and the straight waveguide. After solving it together with the previous equation, we get:

[0053]

[0054] For a steady-state excitation signal E i (t), and after taking Fourier transform of a(t), we get:

[0055]

[0056] Where FT means Fourier transform, and then substituting the above formula into the transfer function of the resonator, we can get:

[0057]

[0058] The relationship between the loss factor and the quality factor in the above formula is:

[0059]

[0060]

[0061]

[0062] Reference Figure 8 , where η represents the loss rate of light in a circle in the microring, and κ represents the amplitude coupling coefficient of transmission. The figure below shows a drop-in multiplexing microring resonator with two output ports. The energy of the microring will be coupled into two straight waveguides respectively.

[0063] Through the same principle and derivation process as above, we can get:

[0064]

[0065] where τ i is the time loss factor caused by the microring resonator's own loss, τ e1 is the time loss factor of the loss caused by the coupling between the microring resonator and the forward propagation waveguide, τ e2 is the loss factor of the coupling between the microring resonator and the counter-propagating waveguide.i , Q e1 , Q e2 are the quality factors of the resonator corresponding to the time loss factor.

[0066] 2.2 Microring Resonator and Differential Equations

[0067] For microring resonators, although equation (12) cannot directly reflect the periodic changes of optical transmission, it is convenient for time-frequency conversion and is more suitable for analysis in the frequency domain and time domain, and for analog optical computing processing analysis. The following is an inverse Fourier transform of the above equation to convert the transmission function into the time domain to obtain the relationship between the input optical signal and the output optical signal:

[0068]

[0069] Where b0 = ω0 / 2Q i +ω0 / 2Q e2 -ω0 / 2Q e1 and a0=ω0 / 2Q i +ω0 / 2Q e1 +ω0 / 2Q e2 , the formula is sorted and eliminated Then you can get:

[0070]

[0071] The above equation is the structure of a first-order linear constant coefficient differential equation. Therefore, the add-drop multiplexing silicon-based microring resonator can be equivalent to a first-order constant coefficient linear differential equation. The coefficients a0 and b0 of the differential equation are determined by the quality factor of the microring resonator, and the quality factor is determined by the length, refractive index, and coupling coefficient of the resonator:

[0072] Q i =-ω0n g L / [cln(1-Y)] (15)

[0073] Q e1 =-ω0n g L / [cln(1-K1)] (16)

[0074] Q e2 =-ω0n g L / [cln(1-K2)] (17)

[0075] From the above theoretical derivation, it can be known that the frequency domain transfer function of the microring resonator is the same as the frequency domain transfer function of the first-order linear time-invariant system. Therefore, the light pulse can be input into the microring resonator, and the output light is equivalent to solving the first-order constant coefficient differential equation for the input pulse light. The coefficients of the differential equation to be solved can be adjusted by changing the parameters of the microring resonator. Temperature can affect the coupling coefficient of the microring resonator, the waveguide refractive index,

[0076] Therefore, the silicon-based microring resonator can be heated by energizing the electrodes, thereby adjusting the parameters of the first-order linear time-invariant system and achieving adjustable coefficients of the differential equation.

[0077] The effect of the present invention can be further illustrated by the following simulation:

[0078] 1. Simulation software:

[0079] Lumerical device software simulation, API system simulation, Matlab numerical calculation

[0080] 2. Simulation content and results:

[0081] In order to verify the effect of electrode heating on the coupling coefficient and resonator cavity Q value of the microring resonator, Lumerical designed a microring coupler with a width of 500nm, a height of 220nm, and a length of 310um. FDTD was used to simulate the refractive index of the microring resonator at different temperatures. FDTD was used to simulate the coupling coefficient between the microring and the waveguide with gap = 0.25um, and then the changes of the differential equation coefficients a0 and b0 at different temperatures were plotted by Matlab according to the formula, as shown in the figure. Figure 4 shown.

[0082] The temperature of the two coupling points of the bifurcated multiplexed microring resonator ranges from 10°C to 110°C, and the adjustable a0 value ranges from 1.5007e10-1.5562e10. The range of b is 4.5343e9-5.6473e9. It can be seen that the a0 value increases linearly with the increase of T1, and the a0 value increases linearly with the increase of T2. The b0 value decreases linearly with the increase of T1, and the a0 value increases linearly with the increase of T2. According to the fitting data, the coefficients of the differential equation solved by the resonator can be changed by adding electrodes.

[0083] In order to verify the effectiveness of the designed silicon-based resonator, the VPI software was used to simulate the design diagram. First, a 10Gb / s Gaussian pulse train was generated using a cascade modulator. Figure 5Then enter the micro-ring resonator system with designed parameters and perform numerical solution of differential equations in the time domain spectrum. Then extract the Gaussian light pulse data generated by the cascade modulator, use Matlab to numerically solve the differential equations, and compare it with the output parameters of the micro-ring resonator after normalization. Figure 6 .

[0084] according to Figure 6 It can be seen that the solution of the first-order linear time-invariant system of Gaussian pulses obtained by VPI simulation is the same as the solution of the differential equation, and the error does not exceed 2%, which means that the designed microring resonator can be applied to the solution of photon differential equations with high accuracy, and can solve differential equations with different coefficients within the adjustment range, and the speed is much higher than that of digital computers.

[0085] Although the principles of the present invention are described in detail above in conjunction with the preferred embodiments of the present invention, those skilled in the art should understand that the above embodiments are merely explanations of the exemplary implementations of the present invention, and are not intended to limit the scope of the present invention. The details in the embodiments do not constitute limitations on the scope of the present invention, and any obvious changes such as equivalent transformations, simple replacements, etc. based on the technical solution of the present invention, without departing from the spirit and scope of the present invention, fall within the protection scope of the present invention.

Claims

1. A variable coefficient differential equation photon computing solution system, characterized in that: It includes a laser, a first modulator, a second modulator, a first amplifier, and a first filter connected in series in sequence; the first modulator is used to modulate the optical signal into a Gaussian function in the time domain; the second modulator is used to realize pulse cutting and is driven by a 10 GHz radio frequency signal emitted by a radio frequency source; The other end of the first filter is connected to the input port of the 3D coupler; one output port of the 3D coupler is connected to the first oscilloscope, and the other output port is sequentially connected to the silicon-based microring resonator chip, the second amplifier, the second filter and the second oscilloscope; the first oscilloscope is used to input the time domain excitation of the differential equation, the second oscilloscope is used to output the normalized numerical solution of the differential equation, and the silicon-based microring resonator chip is used to numerically solve the differential equation; The silicon-based microring resonator chip includes two parallel straight waveguides; a racetrack-type microring resonator coplanar with the two straight waveguides is also provided between the two straight waveguides; electrodes for voltage heating are provided at the angles formed by the microring resonator and the straight waveguide; the incident end of the silicon-based microring resonator is a vertically coupled package of a grating-based optical fiber array, the electrical package is connected to a power supply, and the optical package output end is connected to an oscilloscope; Polarization controllers are arranged between the laser and the first modulator, between the first modulator and the second modulator, and between the 3D coupler and the silicon-based micro-ring resonator chip.

2. The variable coefficient differential equation photon computing solution system according to claim 1, characterized in that: The 3D coupler can be replaced by a splitter / 3 beam splitter.

3. The variable coefficient differential equation photon computing solution system according to claim 2, characterized in that: The first output end and the second output end of the splitter / trimmer are respectively connected to the two corresponding output ends of the 3D coupler in the same manner; the third output end of the splitter / trimmer is connected to the third spectrometer.

4. The variable coefficient differential equation photon computing solution system according to claim 1, characterized in that: The optical packaging output end of the silicon-based microring resonator chip is connected to the input end of the beam splitter, and the two output ends of the beam splitter are respectively connected to the second oscilloscope and the second spectrometer.

5. The variable coefficient differential equation photon computing solution system according to claim 1, characterized in that: Polarization controllers are arranged between the laser and the first modulator, between the first modulator and the second modulator, and between the 3D coupler and the silicon-based micro-ring resonator chip.

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